verifyInclusionExclusion3<T> static method

bool verifyInclusionExclusion3<T>(CustomSet<T> a, CustomSet<T> b, CustomSet<T> c)

Verifies the Inclusion-Exclusion Principle for three sets.

Returns true if: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Example:

final a = CustomSet<int>([1, 2, 3, 4]);
final b = CustomSet<int>([3, 4, 5, 6]);
final c = CustomSet<int>([5, 6, 7, 8]);
print(CardinalityUtils.verifyInclusionExclusion3(a, b, c)); // Output: true

Implementation

static bool verifyInclusionExclusion3<T>(
  CustomSet<T> a,
  CustomSet<T> b,
  CustomSet<T> c,
) {
  final actualUnion = SetOperations.union(
    SetOperations.union(a, b),
    c,
  ).cardinality;
  final calculatedUnion = unionCardinality3(a, b, c);
  return actualUnion == calculatedUnion;
}